On Thursday, June 14, 2018 at 10:32:19 PM UTC-5, Bruce wrote: > > From: Lawrence Crowell <[email protected] <javascript:>> > > > > On Thursday, June 14, 2018 at 7:29:50 AM UTC-5, Bruce wrote: >> >> From: Lawrence Crowell <[email protected]> >> >> I can't make a measurement of energy that is something other than the >> eigenstates or the diagonal form of the Hamiltonian. Energy is the physical >> quantity which defines the einselected basis that is stable in a >> classical-(like) outcome or for the emergence of classicality. >> >> >> That is incorrect. If you are making a position measurement, energy does >> not come into it. Certainly, for many physical system, such as atoms and >> molecules, the energy eigenstates are what one measures. But one measures >> these in the preferred energy basis, which is quite similar to the >> preferred position basis. We are used to a position basis with eigenstates >> as position delta functions along the real line. The preferred energy basis >> is similar, energy delta functions along the real line (remember that we >> can get any real value as the result of a generic energy measurement. >> Energies are quantized only for specific physical systems.) >> >> > I was wondering if you might catch this. I needed more time to reflect on > this and left this open. It is true that the position measurement does not > involve a kinetic energy E = p^2/2m or E = sqrt(p^2 + m^2) term. Things are > not too mysterious with momentum measurements. Is energy completely out of > the loop? Remember that potential energy V = V(x) in most cases. So in the > double slit experiment what happens? The photon or electron wave reaches > the screen and interacts with it. This interaction is going to be position > dependent and I would argue this potential energy is much larger than the > kinetic energy V(x) >> p^2/2m, and so in a decent approximation E = E(x). > Again, this is not the energy of the free particle, but what happens with > the particle interaction with the screen. > > There can be more. In particular if the interaction is of the form V = > ipx, constants ignored. Since px = i/4[(a^†)^2 - a^2 + ħ] this is a > parametric amplification operator and it squeezes the state into the > position basis. > > As a result I still think, though have not worked through anything, that > energy is somehow deeply involved with the einselection of states and the > emergence of a large scale classical world. As for below it is not the case > that we make spectral measurements of atoms or other systems that are in a > basis other than the diagonalization basis for the eigenvalues measured. > > > I don't know why you think that energy is central to einselection. The > idea is that the einselected basis vectors correspond to an operator that > commutes with the interaction Hamiltonian. But that is just the interaction > Hamiltonian, not the full Hamiltonian which could be seen as the energy > operator. So this criterion applies independently for any measured > quantity, be it position, momentum, energy, or anything else. These > einselected bases are not related in any other way. As I have pointed out, > this criterion does not, of itself, tell us what the einselected basis is > -- we have to go to something else for this. > > Bruce >
I might be wrong here, but my point is that energy occurs in discrete eigenvalues and we never measure energy in between. With spin for instance it occurs in any direction and is determined by the orientation of a magnetic field I set. I do not tune some variable to get the energy spectrum of an atom. There is something odd about energy in both quantum mechanics and relativity. LC -- You received this message because you are subscribed to the Google Groups "Everything List" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To post to this group, send email to [email protected]. Visit this group at https://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/d/optout.
